US7215444B2 - Systems and methods for designing zero-shift supercell halftone screens - Google Patents
Systems and methods for designing zero-shift supercell halftone screens Download PDFInfo
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- US7215444B2 US7215444B2 US10/195,424 US19542402A US7215444B2 US 7215444 B2 US7215444 B2 US 7215444B2 US 19542402 A US19542402 A US 19542402A US 7215444 B2 US7215444 B2 US 7215444B2
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
- H04N1/40—Picture signal circuits
- H04N1/405—Halftoning, i.e. converting the picture signal of a continuous-tone original into a corresponding signal showing only two levels
- H04N1/4055—Halftoning, i.e. converting the picture signal of a continuous-tone original into a corresponding signal showing only two levels producing a clustered dots or a size modulated halftone pattern
- H04N1/4058—Halftoning, i.e. converting the picture signal of a continuous-tone original into a corresponding signal showing only two levels producing a clustered dots or a size modulated halftone pattern with details for producing a halftone screen at an oblique angle
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- This invention relates to designing zero-shift supercell halftone screens.
- the most common halftone technique is threshold screening, which compares the image value of each pixel in the original image with one of several predetermined threshold levels that are stored in a halftone screen. If the image value is “darker” than the applied threshold halftone level, a spot of ink or toner is printed at that pixel. Otherwise, the pixel is left unprinted, so that the background color of the image receiving medium is visible. It is well understood in the art that the distribution of printed pixels depends on the design of the halftone screen.
- Halftone screens are typically two-dimensional threshold arrays and are relatively small in comparison to the overall image or document to be printed. Therefore, the screening process uses an identical halftone screen cell repeated for each color separation in a manner similar to tiling.
- the output of the screening process, using a single-cell halftone dot includes a binary pattern of multiple small “dots”, which are regularly spaced and are determined by the size and the shape of the halftone screen.
- the screening output as a two-dimensionally repeated pattern, possesses two fundamental spatial frequencies, which are completely defined by the geometry of the halftone screen.
- FIG. 1 illustrates two halftone supercells that have a non-zero shift. Because supercells are formed by combining a number of halftone cells, supercells can be used to form a “macro” halftone screen for halftoning the original image.
- a supercell is, by definition, larger than the individual halftone cells used to form the supercell, the resulting screen can have more threshold levels and can achieve better visual angles, on average, than the simple cell halftone. Reducing the number of centers in supercells that achieve the desired effects increases the efficiency of the supercell in conserving resources such as, for example, memory, processing power, and the like.
- PostScript hafltoning implementations have difficulty using arbitrary Holladay dots.
- These software implementations of the PostScript standard are usually optimized for PostScript type 3 dots.
- PostScript type 3 dots are zero-shift-square tiles that abut at the corners, as outlined above.
- These software implementations of the PostScript standard also work most efficiently when these square tiles contain a multiple of 32 pixels per tile.
- This invention provides systems and methods for efficiently locating a zero-shift supercell solution for a desired halftone screen.
- This invention separately provides systems and methods for finding zero-shift supercell using a rotated frame of reference.
- This invention separately provides systems and methods that allow a zero-shift supercell solution for a desired halftone screen to be obtained based on printer resolution and desired screen frequency.
- This invention separately provides systems and methods that allow zero-shift supercells to be located based on a desired effective visual area for the base halftone cell.
- This invention separately provides systems and methods for locating zero-shift-halftone solutions based on a desired screen angle.
- a non-square supercell in a first frame of reference has a diagonal that is equal in length to the diagonal of a square supercell in a second frame of reference that is rotated at a desired screen angle to the first frame of reference.
- the screen angle between the first and second frames of reference is a function of the lengths of the sides of the non-square supercell in the first frame of reference.
- the first frame of reference is aligned with the dots that comprise the halftone screen.
- the second frame of reference is aligned with the output device raster.
- a square zero-shift supercell can be designed based on the lengths of the sides of the non-square supercell in the first frame of reference.
- the systems and methods according to this invention can be used to determine one or more sets of side lengths for the non-square rectangle in the first frame of reference based on a desired screen angle between the first and second frames of reference. Then, based on the determined side lengths, a resolution of the image forming device on which the square zero-shift halftone screen is to be used and/or the desired screen frequency, an estimated effective visual area of a base halftone cell can be determined. From this estimated effective visual area of the base halftone cell, a side length for the square zero-shift supercell can be determined and an actual effective visual area for the resulting base halftone cell can be determined. An actual screen frequency based on the actual effective visual area can then be determined.
- the systems and methods of this invention can be used to design the square zero-shift supercell based on a desired area of the square zero-shift supercell, which must be a perfect square of the integer side length of the square zero-shift supercell.
- the area of the zero-shift supercell is a function of the side lengths of the non-square supercell in the first frame of reference and the actual visual area of each base halftone cell of the zero-shift supercell.
- the actual effective visual area of the base halftone cells making up the square zero-shift supercell can be selected such that the supercell area is a perfect square.
- the actual screen frequency of the resulting square zero-shift supercell is a function of the resolution of the image forming device on which the square zero-shift supercell halftone screen will be used and the size of the actual effective visual area of the base halftone cells that make up the square zero-shift supercell.
- FIG. 1 illustrates a pair of 9-center Holladay cells having a non-zero shift
- FIG. 2 illustrates how redundant copies of the Holladay block are used in creating a square zero-shift supercell according to this invention
- FIG. 3 illustrates uniformly tiled square base halftone cells and a first-non-square supercell in a first frame of reference
- FIG. 4 illustrates an exemplary zero-shift supercell formed in a second frame of reference that is rotated relative to the first frame of reference at an angle related to the diagonal of the non-square supercell;
- FIG. 5 illustrates the component vectors that represent the square as exemplary square and non-square supercells of FIG. 3 and FIG. 4 , and the diagonals of the square and non-square supercells;
- FIG. 6 illustrates how the components of the vectors in the second frame of reference relate trigonometrically to the vectors in the first frame of reference
- FIG. 7 is a flowchart outlining a first exemplary embodiment of a method for designing a square zero-shift supercell according to this invention.
- FIG. 8 is a flowchart outlining a second exemplary embodiment of a method for designing a square zero-shift supercell according to this invention.
- FIG. 9 is a flowchart outlining a third exemplary embodiment of a method for designing a square zero-shift supercell according to this invention.
- FIG. 10 is a flowchart outlining a fourth exemplary embodiment of a method for designing a square-shift supercell according to this invention.
- FIG. 11 is a block diagram of a first exemplary embodiment of a system for designing a square zero-shift supercell according to this invention.
- FIG. 12 is a block diagram of a second exemplary embodiment of a system for designing a square zero-shift supercell according to this invention.
- FIG. 13 is a block diagram of a third exemplary embodiment of a system for designing a square zero-shift supercell according to this invention.
- FIG. 14 is a block diagram of a fourth exemplary embodiment of a system for designing a square-shift supercell according to this invention.
- This invention provides systems and methods for designing a halftone screen having a square zero-shift supercell.
- the systems and methods of this invention use a rotated second frame of reference, angled relative to a first frame of reference, provided in units normalized to dot center distances. Accordingly, because the first and second frames of reference are based on a unit cell, rather than in raster units, the exemplary supercell design systems and methods do not require a priori knowledge of the printer resolution.
- FIG. 1 shows a base halftone screen 100 comprising a plurality of square base halftone cells 110 having centers 112 .
- a simple 3,1 Holladay dot 114 can be magnified to form a magnified Holladay block 120 .
- the magnified Holladay block 120 is a 9-center dot. That is, each base halftone cell 110 is considered as a unit cell.
- the area of the simple Holladay block 114 is equal to the combined area of one base halftone cell 110
- the area of the magnified Holladay block 120 is equal to the area of nine base halftone cells 110 .
- This can also be seen intuitively because the corners of the magnified Holladay blocks 120 are centered, at least partially, on the centers 112 of the base halftone cells 110 .
- the sides of the magnified Holladay blocks 120 pass through additional centers 112 of other base halftone blocks 110 .
- the effective area of the magnified Holladay blocks 120 corresponds to the number of centers 112 fully contained within the magnified Holladay block 120 , plus one half the number of centers 112 lying on the edges of the magnified Holladay block 120 , plus one quarter of the number of centers 112 lying on the corners of the magnified Holladay block 120 .
- each of the magnified Holladay blocks 120 fully includes 6 of the centers 112 , while 5 of the centers 112 lie on the edges of the magnified Holladay blocks 120 and 2 centers lie on corners of the magnified Holladay blocks 120 .
- FIG. 2 illustrates the non-special case, where n is not a square number, such that redundant copies of the expanded Holladay block 120 are needed. As shown in FIG. 2 , for most of the Holladay blocks 120 , at least some portion of those Holladay blocks 120 extend outside of the square zero-shift supercell 130 . In particular, in the exemplary embodiment shown in FIG. 2 , only the top-most Holladay block 120 lies entirely within the square zero-shift supercell 130 .
- the portion of one of the pair of Holladay blocks 120 that extends beyond the edge of the square zero-shift supercell 130 is equal in area to the portion of the other Holladay block 120 that lies within the bounds of the square zero-shift supercell 130 . That is, when viewed another way, for each row of Holladay blocks 120 , the portion of a Holladay block 120 that extends beyond the edges of the square zero-shift supercell 130 is equal to the portion of the zero-shift square supercell 130 associated with that row that is not also within that Holladay block 120 .
- a second frame of reference which is rotated by the desired screen angle relative to a first frame of reference, is created.
- the rotated second frame of reference is normalized to the distance between the dot centers, such as the dot centers 112 shown in FIG. 1 and the dot centers 212 shown in FIGS. 3–6 .
- the desired square zero-shift supercell will appear in the rotated second frame of reference as a square rotated to the first frame of reference, where the corners of the square zero-shift supercell are aligned with the dot centers of the base halftone cells 110 .
- FIG. 3 shows a second halftone screen 200 having a plurality of square uniformly sized base halftone cells 210 having centers 212 .
- the halftone screen 200 defines a first frame of reference having an x-axis 202 and a y-axis 204 .
- a non-square halftone supercell 220 can be formed in the halftone screen 200 having integer values for the orthogonal sides 222 and 224 .
- the first side 222 will have a length N
- the second side 224 will have a length M, where N ⁇ M.
- FIG. 4 shows a square supercell 230 aligned to a second frame of reference defined by the x′ axis 206 and the y′ axis 208 superimposed at a desired screen angle ⁇ over the halftone screen 200 shown in FIG. 3 .
- the square zero-shift supercell 230 has two orthogonal sides 232 and 234 having lengths P and Q, respectively.
- the supercell 230 is, by definition, square, the lengths P and Q of the first and second sides 232 and 234 are equivalent.
- the diagonal 226 of the non-square halftone supercell 220 that is aligned with the axes 202 and 204 of the halftone screen 200 is also the diagonal of the square zero-shift supercell 230 .
- P 2 is the area of the square zero-shift supercell 230 .
- N and M are defined in units of the base halftone cells 210 shown in FIG. 4 . That is, M and N are in units of the center-to-center distance between two centers 212 of the base halftone cells 210 in the frame of reference of the halftone screen 200 defined by the x and y axes 202 and 204 .
- the center-to-center distance when squared, is the area associated with a base halftone cell 210 .
- FIG. 5 shows the decomposition of the diagonal 236 of the square zero-shift supercell 230 that is in the second frame of reference defined by the x′ and y′ axes 206 and 208 into x axis and y axis components that are aligned with the x and y axes 202 and 204 of the first frame of reference. That is, as shown in FIG. 5 , the diagonal 236 can be decomposed into the orthogonal sides 222 and 224 of a non-square supercell that is aligned with the centers 212 of the basic halftone cells 210 and the x and y axes 202 and 204 . In the examples shown in FIGS.
- the screen angle ⁇ between the first and second frames of reference which is also the effective visual angle of the halftone screen implemented by the square zero-shift supercell 230
- the line h extending between the centers 212 of two laterally adjacent basic halftone cells 210 can act as the hypotenuse of a right triangle having an interior angle equal to ⁇ , with the other two sides of that triangle aligned with the x′ and y′ axes 206 and 208 of the second frame of reference.
- the other two sides of this small right triangle will have side lengths p and q, respectively.
- Eq. (12) implies that, should the lengths N and M of the sides 222 and 224 of the non-square supercell 220 be known, the screen angle ⁇ between the non-square supercell 220 and the square zero-shift supercell 230 can be determined.
- Eq. (13) implies that, for a desired screen angle ⁇ between the base halftone cells 210 aligned with the first frame of reference defined by the x and y axes 202 and 204 and the square zero-supercell 230 aligned with the second frame of reference defined by the x′ and y′ axes 206 and 208 , once an integer value for N is selected, a (probably) non-integer value M′ can be determined.
- an actual integer value for M can be selected as an integer close to the non-integer value M′.
- the selected value N and the determined value M can then be used to determine the actual screen angle ⁇ and number C of the centers according to Eqs. (11) and (6).
- Eq. (13) could have been developed by solving for N.
- a non-integer value N′ could be determined for a desired value for the screen angle ⁇ and a selected value for M.
- an integer value for N could be selected as an integer close to the non-integer value N′.
- the approximate size of the implementable square zero-supercell 230 can be determined by first estimating the effective visual area A v of a single one of the base halftone cells 210 from the resolution R of the printer on which the square zero-shift halftone screen will be implemented and the desired frequency f of that halftone screen.
- R is the resolution in pixels per inch of the printer on which the halftone screen is to be implemented.
- f is the frequency of that halftone screen in base halftone cells 210 per inch.
- C is the number of centers within the square zero-shift halftone cell 230 .
- the actual effective visual area A v is equal to (600/150) 2 , or 16.
- C is 10.
- the total supercell area A s is 16*10 or 160.
- the approximate side length P′ is thus (160) 5 or 12.6.
- the nearest integer value to 12.6 is 13.
- the side length P of the implementable square shift-supercell 230 is 13.
- the actual supercell area A s is thus 13 2 or 169. Accordingly, the actual effective visual area A v is A s /C, or 169/10 or 16.9.
- the actual frequency f is 600/(16.9) 0.5 or 145.95 dots/inch.
- the effective visual area A v will not be an integer.
- the realizable supercell often will be designed with non-congruent shapes. That is, in various exemplary embodiments, adjacent dot centers within the supercell will not grow identically in shape from level to level. In that case, the angle and/or the frequency of the dot centers would be exact only on average across the entire supercell.
- the effective visual area A v could be selected to be an integer.
- the implementable square zero-shift supercell 230 can be designed with congruent centers.
- the implementable square zero-shift supercell 230 can be made up of 10 congruent copies of the simple 3,1 Holladay dot 114 with 10 pixels each and having an angle ⁇ with a value of 18.43 degrees.
- the simple 3,1 Holladay block in this case would have a width of 10 pixels and a height 7 of one pixel.
- the supercell can be designed with ten identical sub-cells with identical growth sequences and exact angles and frequencies between dot centers.
- the effective visual area A v is selected to be 10, and, M and N are 4 and 2, respectively.
- C is 10 and the supercell area A s is (10*10) or 100.
- the length P of the side of the implementable square zero-shift supercell 230 is (100) 5 , or 10.
- the actual frequency f is 600/(10) 5 or 189.7 dots per inch.
- FIG. 7 is a flowchart outlining a first exemplary embodiment of a method of designing a square-shift supercell according to this invention.
- operation continues to step S 105 , where a desired screen angle ⁇ between the first and second frames of reference is selected.
- step S 110 a desired value for either the first side length N or the second side length M of the non-square supercell in the first frame of reference is selected.
- step S 115 the value for the nominal side length M′ or N′ is determined based on the selected desired screen angle ⁇ and the selected first or second side length N or M. Operation then continues to step S 120 .
- step S 120 the actual side length M or N is selected or determined based on the nominal side length M′ or N′ such that both lengths, as well as the number C of centers in the square zero-shift supercell, will all be integer values.
- step S 125 the actual value for the number C of the centers within the square zero-shift supercell is determined based on the side lengths M and N.
- step S 130 the effective visual area A v of the base halftone cell of the halftone screen being designed is estimated based on the printer resolution and the desired screen frequency. Operation then continues to step S 135 .
- step S 135 the actual supercell area A s is determined based on the estimated effective visual area A v and the number C of the centers that are within the square zero-shift supercell. Then, in step S 140 , the nominal side length P′ of the square zero-shift supercell is determined based on the determined actual supercell area A s . Next, in step S 145 , the actual integer-value side length P is determined based on the nominal side length P′. Operation then continues to step S 150 .
- step S 150 the actual effective visual area A v is determined based on the actual integer-value side length P.
- step S 155 the actual screen frequency f is determined based on the actual effective visual area A v and the printer resolution R. Then, in step S 160 , the method stops.
- FIG. 8 is a flowchart outlining a second exemplary embodiment of a method for designing a square zero-shift supercell according to this invention.
- the steps outlined in FIG. 8 are similar to the steps outlined in FIG. 7 .
- the major difference between the flowcharts outlined in FIGS. 7 and 8 is the order and specific actions performed in steps S 205 –S 220 relative to steps S 105 –S 125 .
- step S 200 operation continues to step S 205 , where a desired value for either the first side length N or the second side length M is selected. Then, in step S 210 , the side length M or the side length N that was not selected or determined in step S 205 is selected such that the number C of centers will be an integer value. Next, in step S 215 , the numbers C of centers within the square zero-shift supercell is determined based on the first and second side lengths M and N selected in steps S 205 and S 210 . Operation then continues to step S 220 .
- step S 220 the screen angle ⁇ between the first and second frames of reference is determined based on the side lengths M and N selected or determined in steps S 205 and S 210 .
- Control then continues to step S 225 .
- steps S 225 –S 255 are identical to steps S 130 –S 160 , respectively, shown in FIG. 6 .
- steps S 225 – 255 will not be described in further detail.
- FIG. 9 is a flowchart outlining a third exemplary embodiment of the method for designing a square zero-shift supercell according to this invention.
- steps S 305 –S 325 are identical to steps S 105 –S 125 of FIG. 7 , as described above. Thus, no further description of these steps will be provided.
- step S 330 the actual effective visual area A v of the base halftone cell of the halftone screen being designed is selected.
- steps S 335 the actual supercell area A s is determined based on the selected actual effective visual area A v and the determined number C of centers.
- step S 340 the nominal side length P′ of the square zero-shift supercell is determined based on the determined actual supercell area A s . Operation then continues to step S 345 .
- step S 345 the actual integer-valued side length P is determined based on the determined nominal side length P′. Then, in step S 350 , the actual screen frequency f is determined based on the selected effective visual area A v and the printer resolution R. Then, in step S 355 , the method ends.
- FIG. 10 is a flowchart outlining a fourth exemplary embodiment of a method for designing a square zero-shift supercell according to this invention.
- steps 405 – 420 are identical to steps S 205 –S 220 described above with respect to FIG. 8 .
- steps S 425 –S 450 are identical to steps S 330 –S 355 outlined above with respect to FIG. 9 .
- steps S 330 –S 355 outlined above with respect to FIG. 9 .
- FIGS. 11–14 are block diagrams outlining first-fourth exemplary embodiments of square zero-shift supercell designing systems 300 – 303 , respectively, according to this invention.
- the square zero-shift supercell designing systems 300 – 303 includes one or more of an input/output interface 310 , a controller 320 , a memory 330 , a first nominal side length determining circuit, routine or application 340 , a first actual side length selecting or determining circuit, routine or application 350 , a center number determining circuit, routine or application 360 , an effective visual area estimating circuit, routine or application 370 , a supercell area determining circuit, routine or application 380 , a second nominal side length determining circuit, routine or application 390 , a second actual side length determining circuit, routine or application 400 , an actual effective visual area determining circuit, routine or application 410 , and an actual screen frequency determining circuit, routine or application 420 , each interconnected by one or more control and/or data bus
- each of the square zero-shift supercell designing systems 300 – 303 is, in various exemplary embodiments, implemented on a programmed general purpose computer. However, in various exemplary embodiments, each of the square zero-shift supercell designing systems 300 – 303 is implemented on a special purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit elements, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmable logic device such as a PLD, PLA, FPGA or PAL, or the like. In general, any device, capable of implementing a finite state machine that is in turn capable of implementing the flowcharts shown in FIGS. 7–10 , can be used to implement the square zero-shift supercell designing system 300 .
- the memory 330 shown in FIGS. 11–14 can be implemented using any appropriate combination of alterable, volatile or non-volatile memory or non-alterable, or fixed, memory.
- the alterable memory whether volatile or non-volatile, can be implemented using any one or more of static or dynamic RAM, a floppy disk and disk drive, a writeable or re-rewriteable optical disk and disk drive, a hard drive, flash memory or the like.
- the non-alterable or fixed memory can be implemented using any one or more of ROM, PROM, EPROM, EEPROM, an optical ROM disk, such as a CD-ROM or DVD-ROM disk, and disk drive or the like.
- each of the circuits, routines and/or applications shown in FIGS. 11–14 can be implemented as portions of a suitably programmed general-purpose computer.
- each of the circuits, routines and/or applications shown in FIGS. 11–14 can be implemented as physically distinct hardware circuits within an ASIC, or using a FPGA, a PLD, a PLA or a PAL, or using discrete logic elements or discrete circuit elements.
- the square zero-shift supercell designing system 300 shown in FIGS. 11–14 can be implemented as software executing on a programmed general purpose computer, a special purpose computer, a microprocessor or the like.
- the particular form each of the circuits, routines and/or application shown in FIGS. 11–14 will take is a design choice and will be obvious and predicable to those skilled in the art.
- the user inputs, using the one or more data input and/or output devices 305 , data defining a desired screen angle ⁇ between the first and second frames of reference.
- the user also inputs a desired value for one of the first and second side lengths N or M using the one or more data input and/or output devices 305 .
- the input/output interface 310 provides this data to the memory 330 , which stores this data.
- the first nominal side length determining circuit, routine or application 340 determines the value for the nominal side length M′ or N′ of the other side based on the screen angle ⁇ and the side length N or M input through the data input and/or output devices 305 and the input/output interface 310 .
- the nominal side length M′ or N′ can be output under control of the controller 310 by the input/output interface 310 to the data input and/or output devices 305 to allow the user to select an actual side length M or N based on the determined nominal side length M′ or N′.
- the first actual side length selecting or determining circuit, routine or application 350 can automatically select or determine the actual side length M or N. This selection or determination can use any one of a number of potential techniques. For example, the integer portion of the nominal side length M′ or N′ determined by the first nominal side length determining circuit or routine could be used as the actual side length. Alternatively, the nominal side length M′ or N′ could be rounded to the nearest integer using standard mathematical techniques.
- the actual side length could be selected based on a table stored in the memory 330 , such as the table set forth below in Table 1.
- Table 1 could be implemented as a lookup table, where the values for M and N are portions of the address to a memory location.
- Table 1 indicates, for a given side value M or N, the potential lengths of the other side N or M that can be selected to provide an integer number of centers.
- the selected side length N or M if the selected side length N or M is even, the actual side length for the other side N or M must also be even.
- the selected side length M or N if the selected side length M or N is odd, the other side length N or M must be odd as well. This occurs because the sum of the squares of M and N itself must be even to ensure the number C of centers is an integer. The sum of the squares will be even if only both squares are even or both squares are odd. Furthermore, each squared number M or N will be even or odd only if the side lengths M and N are even or odd, respectively.
- the center number determining circuit, routine or application 360 determines the number C of centers, as outlined above with respect to Eq. (6).
- the estimated effective visual area is determined by the effective visual area estimating circuit, routine or application 370 .
- the total supercell area is determined using the supercell area determining circuit, routine or application 380 .
- the second nominal side length determining circuit, routine or application 390 determines the nominal side length of the square zero-shift supercell in accordance with Eq. (16).
- the actual side length for the square zero-shift supercell is then selected or determined by the second actual side length determining circuit, routine or application 400 as outlined above with respect to the first actual side length selecting circuit, routine or application 350 .
- the nominal side length is output through the input/output interface 310 to the data input and/or output devices 305 to allow the user to select the actual side length for the square zero-shift supercell.
- the effective visual area determining circuit, routine or application 410 determines the actual effective visual area, as outlined above with respect to Eq. (15).
- the actual screen frequency determining circuit, routine or application 420 determines the actual screen frequency as outlined above with respect to Eq. (14).
- the first actual side length selecting circuit, routine or application 350 and the second actual side length determining circuit, routine or application 400 can be omitted from the first exemplary embodiment of the square zero-shift supercell designing system 300 .
- FIG. 12 shows the second exemplary embodiment of the square zero-shift supercell designing system 301 according to this invention.
- the second exemplary embodiment of the square zero-shift supercell designing system 301 generally contains the same circuit, routine or application elements as the first exemplary embodiment of the square zero-shift supercell designing system 300 .
- the first nominal side length determining circuit, routine or application 340 is omitted entirely, and the first actual side length selection circuit, routine or application 350 can be optionally omitted or included.
- the second exemplary embodiment of the square zero-shift supercell designing system 301 includes an angle determining circuit, routine or application 440 .
- the operation of the second exemplary embodiment of the square zero-shift supercell designing system 301 is identical to the operation of the first exemplary embodiment of the square zero-shift supercell designing system 300 .
- the second exemplary embodiment of the square zero-shift supercell designing system 301 after receiving an input through the data input devices 305 defining the desired value for the first or second side length N or M, the second exemplary embodiment of the square zero-shift supercell designing system 301 , like the first exemplary embodiment of the square zero-shift supercell designing system 300 , either automatically selects or determines the second actual side length using the first actual side length selecting or determining circuit, routine or application 350 , or, by omitting the first actual side length selection circuit, routine or application 350 , receives a further input via the data input and/or output devices 305 defining the other of the side length N or M.
- the angle determining circuit, routine or application 440 determines the screen angle according to Eq. (12). Once the two side lengths M and N and the screen angle ⁇ are defined, the operation of the remaining circuits, routines and/or application 360 – 420 occurs as outlined above with respect to the first exemplary embodiment of the square zero-shift supercell designing system 300 .
- FIG. 13 is a block diagram of the third exemplary embodiment of the square zero-shift supercell designing system 302 according to this invention. As shown in FIG. 12 , the third square zero-shift supercell designing system 302 is generally identical to the first exemplary embodiment of the square zero-shift supercell designing system 300 , except that the effective visual area estimating circuit, routine or application 370 and the effective visual area determining circuit, routine or application 410 are omitted.
- the square zero-shift supercell designing system 302 similarly to the first exemplary embodiment of the square zero-shift supercell designing system 300 , inputs the desired screen angle ⁇ and a first one of the first or second side lengths N or M from the user via the data input and/or output devices 305 and the input/output interface 310 .
- the third exemplary embodiment of the square zero-shift supercell designing system 302 also inputs a selected effective visual area of the base halftone cell from the user through the one or more data input and/or output devices 305 and the input/output interface 310 .
- the first nominal side length determining circuit, routine or application 340 determines a nominal value for the other side length M′ or N′ as outlined above. Then, as outlined above with respect to the first exemplary embodiment of the square zero-shift supercell designing system 300 , the actual value for the side length of the other side M or N is either input by the user via the one or more data input and/or output devices 305 and the input/output interface 310 or is automatically selected or determined using the actual side length selecting or determining circuit, routine or application 350 .
- the center number determining circuit, routine or application 360 operates as outlined above.
- the user has directly supplied a selected value for the effective visual area A v .
- the center number determining circuit, routine or application 360 determines the number C of centers
- the supercell area determining circuit, routine or application 380 , the second nominal side length determining circuit, routine or application 390 and the second actual side length determining circuit, routine or application 400 immediately operated as outlined above with respect to the first exemplary embodiment of the square zero-shift supercell designing system 300 based on the effective visual area value supplied by the user.
- the actual screen frequency determining circuit, routine or application 420 then immediately determines the actual screen frequency, as outlined above with respect to the first exemplary embodiment of the square zero-shift supercell designing system 300 .
- FIG. 14 is a block diagram outlining the fourth exemplary embodiment of the square zero-shift supercell designing system 303 according to this invention.
- the fourth exemplary embodiment of the square zero-shift supercell designing system 303 is identical to the second exemplary embodiment of the square zero-shift supercell designing system 301 , except that, like the third exemplary embodiment of the square zero-shift supercell designing system 302 , the effective visual area estimating circuit, routine or application 370 and the effective visual area determining circuit, routine or application 410 are omitted.
- the fourth exemplary embodiment of the square zero-shift supercell designing system 303 inputs the selected desired value for the first or second side length M or N and then either automatically selects or determines, or alternately inputs, the value for the other of the side lengths M or N, as outlined above with respect to the second exemplary embodiment of the square zero-shift supercell designing system 301 .
- the fourth exemplary embodiment of the square zero-shift supercell designing system 303 also inputs the selected effective visual area from the user through the one or more data input devices 305 and the input/output interface 310 .
- the angle determining circuit, routine or application 440 operates as outlined above with respect to the second exemplary embodiment of the square zero-shift supercell designing system 301 , while the remaining circuits, routines or application 360 , 380 – 400 and 420 operate as outlined above with respect to the third exemplary embodiment of the square zero-shift supercell designing system 302 .
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Abstract
Description
H=√{square root over ((N 2 +M 2))}. (1)
H=√{square root over ((P 2 +Q 2))}. (2)
H=√{square root over ((2P 2))}. (3)
√{square root over ((2P 2))}=√{square root over ((N 2 +M 2))}. (4)
P 2=(N 2 +M 2)/2. (5)
C=(N 2 +M 2)/2. (6)
P=(N*p)−(M*q). (7)
Q=(N*q)+(M*p) (8)
(N*p)−(M*q)=(N*q)+(M*p). (9)
q/p=(N−M)/(N+M). (10)
tan(θ)=q/p. (11)
θ=tan−1((N−M)/(N+M)) (12)
M=N*(1−tan(θ))/(1+tan(θ)). (13)
A v=(R/f)2, (14)
where:
As=Av* C. (15)
P′=√{square root over ((A s))} (16)
TABLE 1 | ||
LENGTH OF |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
LENGTH OF | ||||||||||
|
||||||||||
1 | 1 | x | 5 | x | 13 | x | 25 | x | 41 | x |
2 | x | 4 | x | 10 | x | 20 | x | 34 | x | 52 |
3 | 5 | x | 9 | x | 17 | x | 29 | x | 45 | x |
4 | x | 10 | x | 16 | x | 26 | x | 40 | x | 58 |
5 | 13 | x | 17 | x | 25 | x | 37 | x | 53 | x |
6 | x | 20 | x | 26 | x | 36 | x | 50 | x | 68 |
7 | 25 | x | 29 | x | 37 | x | 49 | x | 65 | x |
8 | x | 34 | x | 40 | x | 50 | x | 64 | x | 82 |
9 | 41 | x | 45 | x | 53 | x | 65 | x | 81 | x |
10 | x | 52 | x | 58 | x | 68 | x | 82 | x | 100 |
Claims (7)
Priority Applications (3)
Application Number | Priority Date | Filing Date | Title |
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US10/195,424 US7215444B2 (en) | 2002-07-16 | 2002-07-16 | Systems and methods for designing zero-shift supercell halftone screens |
JP2003194088A JP4242718B2 (en) | 2002-07-16 | 2003-07-09 | System and method for designing a zero shift supercell halftone screen |
US11/727,506 US20070177214A1 (en) | 2002-07-16 | 2007-03-27 | Systems and methods for designing zero-shift supercell halftone screens |
Applications Claiming Priority (1)
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US10/195,424 US7215444B2 (en) | 2002-07-16 | 2002-07-16 | Systems and methods for designing zero-shift supercell halftone screens |
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US11/727,506 Division US20070177214A1 (en) | 2002-07-16 | 2007-03-27 | Systems and methods for designing zero-shift supercell halftone screens |
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US20040011233A1 US20040011233A1 (en) | 2004-01-22 |
US7215444B2 true US7215444B2 (en) | 2007-05-08 |
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US10/195,424 Expired - Fee Related US7215444B2 (en) | 2002-07-16 | 2002-07-16 | Systems and methods for designing zero-shift supercell halftone screens |
US11/727,506 Abandoned US20070177214A1 (en) | 2002-07-16 | 2007-03-27 | Systems and methods for designing zero-shift supercell halftone screens |
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US11/727,506 Abandoned US20070177214A1 (en) | 2002-07-16 | 2007-03-27 | Systems and methods for designing zero-shift supercell halftone screens |
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JP (1) | JP4242718B2 (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
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US20090060262A1 (en) * | 2007-08-31 | 2009-03-05 | Xerox Corporation | System and method for the generation of multi-layer correlation-based digital watermarks |
US20090060261A1 (en) * | 2007-08-31 | 2009-03-05 | Xerox Corporation | System and method for the generation of correlation-based digital watermarks |
US20120162524A1 (en) * | 2010-12-23 | 2012-06-28 | Ofer Bar-Shalom | Method and apparatus for video frame rotation |
Families Citing this family (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7477421B2 (en) * | 2005-02-04 | 2009-01-13 | Kabushiki Kaisha Toshiba | Halftoning system |
US20060279788A1 (en) * | 2005-06-10 | 2006-12-14 | Monotype Imaging, Inc. | Automatic generation of supercell halftoning threshold arrays for high addressability devices |
Citations (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5124803A (en) * | 1991-02-25 | 1992-06-23 | Ecrm | Method and apparatus for generating digital, angled halftone screens using pixel candidate lists and screen angle correction to prevent moire patterns |
Family Cites Families (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4149194A (en) * | 1977-07-07 | 1979-04-10 | Xerox Corporation | Variable angle electronic halftone screening |
JPH01214710A (en) * | 1988-02-23 | 1989-08-29 | Alps Electric Co Ltd | Measuring method for azimuth and apparatus therefor |
US4987496A (en) * | 1989-09-18 | 1991-01-22 | Eastman Kodak Company | System for scanning halftoned images |
JP3876531B2 (en) * | 1998-05-28 | 2007-01-31 | 富士通株式会社 | Document image skew correction method |
JP2001018376A (en) * | 1999-07-09 | 2001-01-23 | Canon Inc | Recorder and recording method |
US20030107768A1 (en) * | 2001-12-04 | 2003-06-12 | Crounse Kenneth R. | Halftoning with uniformly dispersed dot growth |
-
2002
- 2002-07-16 US US10/195,424 patent/US7215444B2/en not_active Expired - Fee Related
-
2003
- 2003-07-09 JP JP2003194088A patent/JP4242718B2/en not_active Expired - Fee Related
-
2007
- 2007-03-27 US US11/727,506 patent/US20070177214A1/en not_active Abandoned
Patent Citations (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5124803A (en) * | 1991-02-25 | 1992-06-23 | Ecrm | Method and apparatus for generating digital, angled halftone screens using pixel candidate lists and screen angle correction to prevent moire patterns |
Non-Patent Citations (1)
Title |
---|
T. M. Holladay, "An Optimum Algorithm for Halftone Generation for Displays and Hard Copies," Proceedings of the SID, vol. 21/2, pp. 185-192, 1980. |
Cited By (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20090060262A1 (en) * | 2007-08-31 | 2009-03-05 | Xerox Corporation | System and method for the generation of multi-layer correlation-based digital watermarks |
US20090060261A1 (en) * | 2007-08-31 | 2009-03-05 | Xerox Corporation | System and method for the generation of correlation-based digital watermarks |
US8077907B2 (en) * | 2007-08-31 | 2011-12-13 | Xerox Corporation | System and method for the generation of correlation-based digital watermarks |
US8098880B2 (en) * | 2007-08-31 | 2012-01-17 | Xerox Corporation | System and method for the generation of multi-layer correlation-based digital watermarks |
US20120162524A1 (en) * | 2010-12-23 | 2012-06-28 | Ofer Bar-Shalom | Method and apparatus for video frame rotation |
US8718406B2 (en) * | 2010-12-23 | 2014-05-06 | Marvell World Trade Ltd. | Method and apparatus for video frame rotation |
Also Published As
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JP2004056800A (en) | 2004-02-19 |
US20070177214A1 (en) | 2007-08-02 |
JP4242718B2 (en) | 2009-03-25 |
US20040011233A1 (en) | 2004-01-22 |
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